GATE (TF) Textile 2013 Question Paper Solution | GATE/2013/TF/21

Q: What is the formula for F the ratio?

The F ratio, also known as the F-statistic, is a statistical measure used in analysis of variance (ANOVA) to compare the variability between groups to the variability within groups. The formula for the F ratio is: F = MSB / MSW where: MSB is the mean square between groups, which is the sum of squares between groups divided by the degrees of freedom between groups. MSW is the mean square within groups, which is the sum of squares within groups divided by the degrees of freedom within groups. The formula for calculating the F ratio in terms of standard deviation can be derived from the formula in terms of variance. The variance is the square of the standard deviation. So, if we denote the standard deviation between groups as σB and the standard deviation within groups as σW, the formula for the F ratio in terms of standard deviation would be: F = (σB^2) / (σW^2) where σB is the standard deviation between groups, and σW is the standard deviation within groups and σB is greater than σW.

Question 21 (Textile Engineering & Fibre Science)

Two yarn samples have standard deviation of strength $\sigma_1$ and $\sigma_2$ . If $\sigma_1 < \sigma_2$ , the $'F'$ ration would be

(A)	$\frac{\sigma_1}{\sigma_2}$
(B)	$\frac{\sigma_2}{\sigma_1}$
(C)	$\frac{\sigma_1^2}{\sigma_2^2}$
(D)	$\frac{\sigma_2^2}{\sigma_1^2}$

Answer / Solution

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Option D

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What is the formula for F the ratio?

The F ratio, also known as the F-statistic, is a statistical measure used in analysis of variance (ANOVA) to compare the variability between groups to the variability within groups. The formula for the F ratio is:
F = MSB / MSW
where:
MSB is the mean square between groups, which is the sum of squares between groups divided by the degrees of freedom between groups.
MSW is the mean square within groups, which is the sum of squares within groups divided by the degrees of freedom within groups.

The formula for calculating the F ratio in terms of standard deviation can be derived from the formula in terms of variance.
The variance is the square of the standard deviation. So, if we denote the standard deviation between groups as σB and the standard deviation within groups as σW, the formula for the F ratio in terms of standard deviation would be:
F = (σB^2) / (σW^2)
where σB is the standard deviation between groups, and σW is the standard deviation within groups and σB is greater than σW.

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